Uses
Ways to express a Ratio
Suppose we are taking a ratio of Variable A to Variable B where
Variable A = 5 and
We can express this ratio in one of the two forms shown in the flowchart below. Note that A is taken to be synonymous with the value of Variable A and likewise for B.
Different Forms of Ratios and How to Interpret Them
Although the interpretation for the first ratio expression is more straight-forward, expressing a ratio as a decimal normalises the denominator (or variable B) to 1. Such normalisation facilitates the comparison of two or more ratios, such as comparison across time or across groups. For example, it is easier to interpret the difference between the ratios 1.25 and 1.50, instead of 5:4 and 3:2.
Another point to note is that ratios do not normally have units, especially when the two variables share the same units.
Example 1: Using ratios
Suppose we are comparing the wages for two occupations, A and B.
Suppose the median monthly wage for occupation A is $2,000 and that for occupation B is $3,000. In this case, the ratio in decimal form is $2,000/$3,000 = 0.67. As the ratio is less than 1, this means the median wage for occupation A is less than the median wage for occupation B. Note further that the ratio has no units since the median wage for both occupations A and B are in dollars.
Occupation A Has Lower Median Wage Than Occupation B
Suppose instead that the median wage for occupations A and B are both $3,000. The ratio of the wages in decimal form is 1.00, implying that the quantities compared have the same value.
Occupation A Has the Same Median Wage as Occupation B
Finally, suppose the median wage for occupation A is $3,000 and that for occupation B is $2,000. The ratio of the wages in decimal form is 1.50, which exceeds 1. This means that the first quantity (here, median wage of occupation A) is larger than the second quantity (median wage of occupation B).
Occupation A Has Higher Median Wage Than Occupation B
